I am looking for the best way to retrieve the next and previous records of a record without running a full query. I have a fully implemented solution in place, and would like to
In general, I denormalize the data from the indexes. They may be stored in the same rows, but I almost always retrieve my result IDs, then make a separate trip for the data. This makes caching the data very simple. It's not so important in PHP where the latency is low and the bandwidth high, but such a strategy is very useful when you have a high latency, low bandwidth application, such as an AJAX website where much of the site is rendered in JavaScript.
I always cache the lists of results, and the results themselves separately. If anything affects the results of a list query, the cache of the list results is refreshed. If anything affects the results themselves, those particular results are refreshed. This allows me to update either one without having to regenerate everything, resulting in effective caching.
Since my lists of results rarely change, I generate all the lists at the same time. This may make the initial response slightly slower, but it simplifies cache refreshing (all the lists get stored in a single cache entry).
Because I have the entire list cached, it's trivial to find neighbouring items without revisiting the database. With luck, the data for those items will also be cached. This is especially handy when sorting data in JavaScript. If I already have a copy cached on the client, I can resort instantly.
To answer your questions specifically:
Also, when you cache things, cache them at the most generic level possible. Some stuff might be user specific (such as results for a search query), where others might be user agnostic, such as browsing a catalog. Both can benefit from caching. The catalog query might be frequent and save a little each time, and the search query may be expensive and save a lot a few times.